Yes when you have anxiety or having an anxiety attack or panic attack you can experience chest tightness and sometimes you may feel like the chest tightness is leading to a heart attack.
But usually when you're experiencing chest tightness during anxiety or an anxiety attack or panic attack the chest tightness is usually harmless and doesn't mean a heart attack.
You should try to calm down of if it's someone else experiencing the chest tightness then you should try to get them to calm down and breath slow deep breaths.